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Calculus Based Physics Question

  1. Mar 1, 2013 #1
    1. The problem statement, all variables and given/known data A 3kg box is held up high in the air by a a rope with negligible mass. The rope's tension is depends on the function of time T(t) = (36N/s)*t. The box is at rest at t = 0. Only the forces tension and gravity act on this box.

    a) What is the velocity at t = 1.0s?
    b) What is the velocity at t = 3.0s?

    2. Relevant equations

    I think that my acceleration formula is the problem, but I don't know why.

    a(t) = (2.2m/s^3)t - 9.8m/s^2 I took out the mass to get the box's acceleration and then I just broke up the applied acceleration from the constant gravitational acceleration.

    v(t) = (1.1m/s^3)t^2 - (9.8m/s^2)t This is my integral of the acceleration.

    3. The attempt at a solution

    a) a(1s) = 1.1m/s - 9.8m/s = -8.7m/s but the book's answer is -3.8m/s.

    I just can't grasp how I am wrong.
     
  2. jcsd
  3. Mar 1, 2013 #2
    How did you get 2.2 m/s^3 from 36 N/s?
     
  4. Mar 1, 2013 #3
    ƩFy = T - mg = ma; a = 12m/s^2 - 9.8m/s^2 = 2.2m/s^2, so I divided out the mass to get the box's acceleration of 12m/s^2. Then, I ...

    Lol, ok, in my attempt to answer your question I see how it can work I can get the right answer. Thanks for asking :)
     
  5. Mar 1, 2013 #4
    You are welcome :)
     
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